St Alban's High School NUMERACY
ACROSS THE CURRICULUM
Numeracy is a proficiency that involves confidence and
competence with numbers and measures. It requires an
understanding of the number system, a repertoire of
computational skills and an inclination and ability to solve
number problems in a variety of contexts. Numeracy also demands practical
understanding of the ways in which information is gathered by counting and
measuring, and is presented in graphs, diagrams, charts and tables.
Mathematical skills can be consolidated and enhanced when pupils have
opportunities to apply and develop them across the curriculum. Poor numeracy
skills, in particular, hold back pupils' progress and can lower their self-esteem. To
improve these skills is a whole-school matter. Each department should identify the
contribution it makes towards numeracy and other mathematical skills so that
pupils become confident at tackling mathematics in any context.
The school policy is that:
Numeracy is a key skill in students' learning and all students are entitled to quality
experiences in this area and that the teaching of numeracy is the responsibility of
all staff and the school's approaches should be as consistent as possible across the
curriculum.
Curriculum areas will endeavour to ensure that materials presented to students will
match their capability both in subject content and in numerical demands. They will
liase with the Special Needs and Mathematics departments when appropriate in
order to support their teaching of numeracy.
All teachers should consider pupils' ability to cope with the numerical demands of
everyday life and provide opportunities for students to:
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handle number and measurement competently, mentally, orally and in writing;
use calculators accurately and appropriately;
interpret and use numerical and statistical data represented in a variety of
forms.
Making links between mathematics and other subjects
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You need to look for opportunities for drawing mathematical experience out of a
wide range of children's activities. Mathematics contributes to many subjects of
the curriculum, often in practical ways. Activities such as recording the growth of a
plant or an animal, measuring temperature and rainfall, or investigating the cog
wheels in a bicycle can provide data or starting points for discussion in your
mathematics lessons as well as opportunities to apply and use mathematics in real
contexts.
English:
Mathematics lessons can help to develop and support pupils' literacy
skills: for example, by teaching mathematical vocabulary and
technical terms, by asking children to read and interpret problems
to identify the mathematical content, and by encouraging them to
explain, argue and present their conclusions to others. Equally, English lessons can
support your mathematics lesson. For example non-fiction texts can be chosen in
which mathematical vocabulary, graphs, charts and tables have to be interpreted.
An identified opportunity exists in Year 9
Advertising Unit – Pie Charts/Graphs representing sales/demand for products and
cost of campaigns
Science:
Almost every scientific investigation or experiment is likely to
require one or more of the mathematical skills of classifying,
counting, measuring, calculating, estimating, and recording in tables
and graphs. In science pupils will, for example, order numbers,
including decimals, calculate means and percentages, use negative numbers when
taking temperatures, substitute into formulae, re-arrange equations, decide which
graph is the most appropriate to represent data, and plot, interpret and predict
from graphs.
An identified opportunity exists in Year 8:
Distance time graphs, representing speed – See PE
Discuss range of formulae used – re-arranging and substitution a possibility
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An identified opportunity exists in Year 7
Line - Temperature against time graph demonstrating a cooling liquid
Bar – Cancer against cigarettes smoked
Art, Design and Technology:
Measurements are often needed in art and design and technology. Many
patterns and constructions are based on spatial ideas and properties of
shapes, including symmetry. Designs may need enlarging or reducing,
introducing ideas of multiplication and ratio. When food is prepared a
great deal of measurement occurs, including working out times, adapting
recipes, and calculating cost; this may not be straightforward if only
part of a packet of ingredients has been used.
An identified opportunity exists in Year 8 Design and Technology:
2D representations of 3D objects – Isometric drawings, plan and elevation drawings
to scale.
Graphs from questionnaires
Information and Communications Technology:
Children will apply and use mathematics in a variety of ways
when they solve problems using ICT. For example, they will
collect and classify data, enter it into data handling software,
produce graphs and tables, and interpret and explain their
results. Their work in control includes the measurement of
distance and angle, using uniform non- standard then standard measures. When
they use computer models and simulations they will draw on their abilities to
manipulate numbers and identify patterns and relationships.
An identified opportunity exists in Year 7
Use of formulas in spreadsheets – predicting outcomes
An identified opportunity exists in Year 8
Representing weather data – interpretation of the various graphs and discussion as
to which ones are valid and why.
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History, Geography and Religious Education:
In history and geography children will collect data by counting and
measuring and make use of measurements of many kinds. The study of
maps includes the use of co-ordinates and ideas of angle, direction,
position, scale and ratio. Historical ideas require understanding of
the passage of time. which can be illustrated on a time line. similar to
the number line that they already know.
An identified opportunity exists in Year 7 Geography
Use of scale in reading maps and drawings of bedroom
Pie Charts or divided bar charts
An identified opportunity exists in Year 8 Geography
Climate graphs
An identified opportunity exists in Year 9 Geography
Development indicator graphs (Scatter graphs)
An identified opportunity exists in Year 7 RE
Possible to survey how widely available are fair trade goods in shops.
An identified opportunity exists in Year 9 RE
Possible to make use of surveys and results regarding the environment.
An identified opportunity exists in Year 9 History
Graphs of weapons and ships available during the 1st and 2nd world war –
interpretation of the graphs.
Physical Education and Music:
Athletic activities require measurement of height, distance, time
and speed, while ideas of time, symmetry, movement. position and
direction are used extensively in music. dance, gymnastics and
ball games.
The key to making the most of all these opportunities is to identify the
mathematical possibilities across the curriculum at the planning stage. You should
also draw children's attention to the links between subjects by talking frequently
about them, both in Mathematics and in other lessons.
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Identified opportunities exist in Years 7,8 and 9 PE
Angle of elevation of shot putt, discuss, javelin, hitting softball – link with
substituting into formulas and drawing graphs.
Timing of distances in athletics - link with distance time graphs (take split times)
Compare different events, average speed, real life graphs, compare with world
records.
Scale drawing of the sports hall and of different courts. Problem solving exercise
such as we need a sports hall that allows us to play 5 games of badmington etc…
what are the possible sizes of the sports hall?
Scale drawing of an athletics field.
Modern Foreign Languages
An identified opportunity exists in Year 7
Drawing and interpretation of ‘happiness’ graphs using correct vocabulary
An identified opportunity exists in Years 8 and 9
Drawing and interpretation of conversion graphs using correct vocabulary
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Cross-curricular guidance:
This document should provide information and guidelines to help produce
consistency across the curriculum - it is not intended to be a prescription for
teaching although some advice is given.
Approaches
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It is recognised that not all students in a teaching group will have the same
numerical skills and where unsure of an appropriate 'numerical level' teachers
will consult with the Mathematics Department.
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All teachers will discourage students from writing down answers only and
encourage students to show their numerical working out within the main body of
their work.
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All teachers will encourage the use of estimation particularly for checking work.
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All teachers will encourage students to write mathematically correct
statements.
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It is recognised that there is never only one correct method and students will
be encouraged to develop their own correct methods where appropriate rather
than be taught 'set' ways.
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Wherever possible students will be allowed and encouraged to 'vocalise' their
maths - a necessary step towards full understanding for many students.
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All students should be helped to understand the methods they are using or
being taught - students gain more and are likely to remember much more easily
if they understand rather than are merely repeating by rote.
Calculators:
In order to improve numeracy skills, it is essential that students
should be encouraged to use non-calculator methods whenever
possible. However departments should ensure students have
access to calculators when they are necessary.
It is recognised that where calculators are to be used their
correct use may have to be taught.
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The Maths department sell Sharp calculators using the D.A.L. system of display, e.g
you type in Sin 38 not 38 sin. Where appropriate it would be helpful if other
departments used similar calculators.
Methods and Presentation:
Where a student is gaining success with a particular method it is important that
s/he is not confused by being given another method. This does not disallow the
possibility of introducing alternatives in order to improve understanding or as part
of a lesson deliberately designed to investigate alternative methods, provided
students can manage this without confusion.
Working out:
In all arithmetic, the importance of place value and neat column keeping should be
stressed.
In a line of workings an "equals" sign should only appear once.
This is poor practice:
£3.50 x 0.85  2.975 + 3.50  6.475  £6.48
This is good practice:
£3.50 x 0.85  2.975
2.98 + 3.50  £6.48
Language:
When referring to decimals say "three point one four" rather than "three point
fourteen".
Read numbers out in full, so say three thousand four hundred rather than three,
four, zero, zero.
It is important to use the correct mathematical term for the type of average being
used, ie. mean, median or mode.
Mean
Total of values of sample  sample size.
[The term average is commonly used when referring to the mean]
Median
Mode
Middle value of sample when sample values are arranged in order
size.
Sample values which occur most frequently.
Checking:
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Encourage students to check divisions by multiplication and subtractions by adding.
Rough Conversions between Metric and Imperial:
In the Maths Department we teach the following conversions:
1 inch  2.5 cm
1 yard  1 m
1 kg  2.2 lbs
2 pints  1 litre
1 mile  1.6 km
1 oz  25 g
Pupils should be expected to record the units they are using when answering a
question.
Standard Form:
Students need to be aware of how their calculators express standard form and
what it means. E.g. on some calculators 5  200  2.52
It should be noted that this should be recorded as 2.5 x 10-2 and that it is
equivalent to 0.025
Multiples of ten:
When multiplying by ten do not teach the 'rule' add a nought or move the decimal
point along one but rather explain that the numbers move one place to the left
relative to the decimal place. So
3 . 6 4 x 10
=36.4
Time:
Pupils should never record 3hrs and 30 mins as 3.30hrs but as 3.5hrs.
[When working with time it is possible to use the degrees/mins/secs key on many
calculators.]
Equations:
The terms "cross-multiply" and “swap sides – swap signs” can lead to
misunderstandings, as part of any explanation of how to solve equations and so
should be avoided.
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To teach solution of linear equations we use the 'balancing method' or a flow
diagram
To solve: 3x – 7 = 5
Balance Method: 3x – 7  5
3x – 7 + 7  5 + 7
3x  12
3x  3  12 3
x4
(add 7 to both sides)
(divide both sides by 3)
Flow Chart Method:
START:
END:
x  x3  -7  3x - 7 (you now UNDO)
4  3  +7  5
X=4
Guidelines for Constructing/Using Graphs and Charts
Students should be encouraged to:
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use a sharp pencil.
label both axes and give a title
use independent variable on x-axis, and dependant variable
on the y-axis, eg: if graphing temperature of a cooling liquid, time should go on
the x-axis and temperature on the y-axis. [The temperature of the liquid is
dependant on the time of the reading.]
label lines not spaces, unless a bar-chart with discrete data
use equally spaced intervals
use convenient scales
mark points by a small cross not a dot
draw graphs on squared or graph paper
to draw graphs of a sensible size (they tend to make them too small)
Pupils should be exposed to Bar Charts, Pie Charts, Pictograms, Line graphs and
Cumulative frequency curves. Histograms are only tackled by higher level students.
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Students need to be taught when each type of graph is appropriate. (This is very
important as students will generally produce the type of graph they last met
without much thought to appropriateness.)
Bar-charts
the bars should be of equal width and equally spaced
the bars do not have to touch for discrete data
frequency should be on the y (vertical) axis.
Discrete data
Data is described as discrete if specific values only can be used, eg. shoe size is
discrete as sizes such as 4.8 and 5.77 cannot exist.
Continuous data
Data is described as continuous if all values can exist, eg. height and weight are
continuous data as potentially any value could be measured.
Pie Charts
Sectors should be labelled (eg. Car, Blue….) or there should be a key.
Do not be surprised if the total of all the angles is 360 plus or minus one or two
degrees. This will almost certainly be due to the rounding that may be necessary.
In these cases either add or take the one or two degrees from the largest angle.
Histograms
Do not use the term Histogram unless the bar widths are unequal and relative
frequency is plotted along the y axis. This is only taught to those in the top set in
Years 10 and 11. Students need to appreciate the connection between the area and
the frequency.
Scaling
If axes do not start from zero, a break represented by a zig-zag line should be
shown on the axis.
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